Councils in London have privately warned that low-income families will be driven out of richer neighbourhoods to the suburban fringes and parts of the deprived inner city, putting pressure on social services and schools and potentially "triggering a spiral of debt, eviction and homelessness".

Freedom of information requests to London boroughs revealed the disturbing consequences of government housing measures since July. The main measures cap payments to private landlords by councils for benefit claimants from next April – with four-bedroom homes limited to £400 a week. Six months later all rents paid from the public purse will be pegged to a third of market rates, down from a half. Claimants of jobseeker's allowance will lose 10% of housing benefit from 2013. Places such as Oxford, Blackpool and Brighton will be affected but the capital will bear the brunt of the changes.

George Osborne says the taxpayer should not be expected to pay for families to live in expensive city centres, but many councils have balked at the proposals. London boroughs estimate that 82,000 families – more than 200,000 people – face losing their homes because private landlords, enjoying a healthy rental market buoyed by young professionals who cannot afford to buy, will not cut rents to the level of caps imposed by ministers.

The result would be "social flight" to poorer parts of the capital as the reforms, according to one local authority, "effectively make it impossible for low-income households to rent in the private sector in inner London".

The Labour leader of Haringey council, Clare Kober, said other London councils have been buying up leases in the borough in anticipation of having to house their claimants in cheaper areas.

"It's segregating the capital which is extremely problematic for social cohesion and puts real pressure on services here. In the last two months we have seen an influx of 40 children on child protection plans. That's more than a 10% rise for us in vulnerable children … which means other services come under pressure," said Kober, who led the council through the Baby P crisis.

Haringey's new residents may have moved from Camden, which said benefit caps would "shunt the cost of health, social care and education services for vulnerable families to neighbouring boroughs – in particular Islington, Haringey, Brent, Barnet and Enfield". The £400 a week was £1,600 less than the current "ceiling payment" and more than 800 families with children would be affected.

The question goes beyond party affliation. Lynne Hillan, leader of Barnet, the Tory borough with claims to a no frills model, wrote last week to Eric Pickles, the communities and local government secretary, to warn the cuts may see tenants "fall into arrears and face eviction, leading to an increase in the numbers of homeless families" and that "high-rent inner London boroughs may seek to place more families in accommodation in Barnet, placing additional pressure on public service(s)."

Next door in Enfield, councillors predicted an "increase in overcrowding in the private rented sector as families are forced to move into cheaper rented homes with four bedrooms or less". This effect may be replicated in inner London as families on welfare squeeze into smaller properties to keep benefits.

Newham said it was "experiencing high levels of antisocial behaviour as a direct result of the saturation of the private rented sector in many neighbourhood areas". Although the government has proposed to compensate councils for the upheaval, Lewisham said this "will be nowhere near enough to cover the potential shortfalls between rent and housing benefit entitlement due to the changes."

There is evidence to dispute the idea that the taxpayer has been funding the "lifestyle choices" of those on benefits and that the reforms will disproportionately hit minority and religious groups. Hackney says of the 32 claimants living in five-bedroom properties who would lose £1,200 a month, "94% (31) are from the [orthodox] Charedi Jewish community".

Karen Buck, the Labour MP for Westminster North and shadow welfare minister, who raised the alarm over the "social cleansing" of London, said the "sheer speed and scale of the cuts across the country but especially London will see local councils left with the responsibility of finding homes and providing services for tens of thousands of households. These are families, vulnerable families often with children".